615 Final Project
Ningze Zu
12/7/2018
Abstract
In this project, I will use benford’s law to analysis the distribution of Airbnb listings’ price in Seattle and perform an exploratory data analysis figure out other features that are relevant to the rental price of Airbnb.
Price Distribution & Benford’s Law
Figure 1 below shows the price distribution of Airbnb listings in Seattle. The plot displays a normal distribution but a little right skewness. It shows a high concentration of listing prices between 0 and 200 USD.
To validate the data against Benford’s law, I using the first two digits to analysis ‘benford’. The main results and plots of the analysis are shown below:
In the plots, the original data is in blue, and the expected Benford’s distribution is in red. We can see from the first plot that the Airbnb rental price in Seattle do have a tendency to follow the Benford’s Law. However, there are also some clear discrepancies.
The print result of the analysis displays the main statistics of the data. We can see that the mean value is close to 0.5. It shows the five largest discrepancies and some results of statistical tests like Chi-squared test as well. The p-value is pretty small, but we cannot focus on p-value only.
bf <- benford(airbnb_se_m$price)
plot(bf)
bf##
## Benford object:
##
## Data: airbnb_se_m$price
## Number of observations used = 8610
## Number of obs. for second order = 364
## First digits analysed = 2
##
## Mantissa:
##
## Statistic Value
## Mean 0.48
## Var 0.11
## Ex.Kurtosis -1.43
## Skewness 0.15
##
##
## The 5 largest deviations:
##
## digits absolute.diff
## 1 15 239.67
## 2 99 237.42
## 3 10 230.61
## 4 12 227.70
## 5 75 195.47
##
## Stats:
##
## Pearson's Chi-squared test
##
## data: airbnb_se_m$price
## X-squared = 7826.1, df = 89, p-value < 2.2e-16
##
##
## Mantissa Arc Test
##
## data: airbnb_se_m$price
## L2 = 0.057452, df = 2, p-value < 2.2e-16
##
## Mean Absolute Deviation: 0.007389969
## Distortion Factor: 2.066781
##
## Remember: Real data will never conform perfectly to Benford's Law. You should not focus on p-values!Next, I extract the observations with the largest discrpencies and plot the price distribution.
suspects <- getSuspects(bf, airbnb_se_m)
head(suspects)## X id name host_id
## 1: 30 24212 ★PERFECT Getaway w/ Views★SALE 10/8, 11 74305
## 2: 52 103908 Green Lake Gem - Walk to Lake 541406
## 3: 61 132160 Green Lake Guest Suite, private apt 558743
## 4: 81 202174 Modern Townhome in Superb Location 58235
## 5: 83 202260 Cozy Seattle Apartment Near UW & Children's 990195
## 6: 84 208356 contemporary art loft downtown [7] 1025723
## host_is_superhost street neighbourhood_cleansed
## 1: f Seattle, WA, United States Belltown
## 2: f Seattle, WA, United States Green Lake
## 3: t Seattle, WA, United States Green Lake
## 4: f Seattle, WA, United States International District
## 5: f Seattle, WA, United States View Ridge
## 6: t Seattle, WA, United States International District
## city state zipcode country_code latitude longitude property_type
## 1: Seattle WA NA US 47.61540 -122.3487 Condominium
## 2: Seattle WA NA US 47.68427 -122.3266 Apartment
## 3: Seattle WA NA US 47.68226 -122.3434 Guest suite
## 4: Seattle WA NA US 47.59605 -122.3179 Townhouse
## 5: Seattle WA NA US 47.68004 -122.2840 Apartment
## 6: Seattle WA NA US 47.59908 -122.3256 Loft
## room_type accommodates bathrooms bedrooms beds
## 1: Entire home/apt 6 1.0 2 3
## 2: Entire home/apt 4 1.0 1 1
## 3: Entire home/apt 6 1.0 2 3
## 4: Entire home/apt 4 2.0 2 2
## 5: Entire home/apt 2 1.0 1 1
## 6: Private room 2 1.5 1 1
## amenities
## 1: {TV,"Cable TV",Internet,Wifi,"Air conditioning","Wheelchair accessible",Pool,Kitchen,"Free parking on premises",Gym,Elevator,"Hot tub",Heating,"Family/kid friendly",Washer,Dryer,"Smoke detector","Carbon monoxide detector","Fire extinguisher",Essentials,Shampoo,"24-hour check-in",Hangers,"Hair dryer",Iron,"Laptop friendly workspace","Hot water","Long term stays allowed","Host greets you"}
## 2: {TV,"Cable TV",Internet,Wifi,Kitchen,"Free street parking","Buzzer/wireless intercom",Heating,"Family/kid friendly",Washer,Dryer,"Smoke detector","Carbon monoxide detector","First aid kit","Safety card","Fire extinguisher",Essentials,Shampoo,Hangers,"Hair dryer",Iron,"Laptop friendly workspace","Private entrance","High chair",Crib,"Hot water",Other}
## 3: {TV,Internet,Wifi,"Air conditioning",Kitchen,"Free street parking",Heating,Washer,Dryer,"Smoke detector","Carbon monoxide detector","First aid kit","Fire extinguisher",Essentials,Shampoo,"24-hour check-in",Hangers,"Hair dryer",Iron,"Laptop friendly workspace","translation missing: en.hosting_amenity_49","Self check-in",Keypad,"Private entrance","Room-darkening shades","Hot water","Bed linens","Extra pillows and blankets",Microwave,"Coffee maker",Refrigerator,Dishwasher,"Dishes and silverware","Cooking basics",Oven,Stove,"BBQ grill","Patio or balcony","Luggage dropoff allowed","Wide hallway clearance","Wide doorway","Well-lit path to entrance","Lake access","Handheld shower head"}
## 4: {TV,"Cable TV",Internet,Wifi,Kitchen,"Free parking on premises","Smoking allowed","Free street parking",Heating,Washer,Dryer,"Smoke detector","Carbon monoxide detector","Safety card",Essentials,Shampoo,Hangers,"Hair dryer",Iron,"Self check-in",Lockbox,"Private entrance",Bathtub,"Hot water","Bed linens","Extra pillows and blankets","Coffee maker",Refrigerator,Dishwasher,"Dishes and silverware","Cooking basics",Oven,Stove,"BBQ grill","Patio or balcony","Garden or backyard","Luggage dropoff allowed","Long term stays allowed","Step-free access","Flat path to front door","Well-lit path to entrance","Handheld shower head"}
## 5: {Internet,Wifi,Kitchen,"Free parking on premises","Pets live on this property",Dog(s),"Indoor fireplace",Heating,Washer,Dryer,"Smoke detector","Carbon monoxide detector","First aid kit","Safety card","Fire extinguisher",Essentials,Shampoo,"24-hour check-in",Hangers,"Hair dryer",Iron,"Laptop friendly workspace","translation missing: en.hosting_amenity_49","translation missing: en.hosting_amenity_50","Private entrance"}
## 6: {TV,"Cable TV",Internet,Wifi,"Air conditioning",Kitchen,"Paid parking off premises",Heating,"Smoke detector","Carbon monoxide detector","First aid kit","Safety card","Fire extinguisher",Essentials,Shampoo,"Lock on bedroom door","24-hour check-in",Hangers,"Hair dryer",Iron,"Laptop friendly workspace","translation missing: en.hosting_amenity_49","translation missing: en.hosting_amenity_50","Self check-in",Lockbox,"Private living room","Hot water","Bed linens","Extra pillows and blankets",Microwave,"Coffee maker",Refrigerator,"Dishes and silverware","Luggage dropoff allowed"}
## price security_deposit cleaning_fee minimum_nights maximum_nights
## 1: 157 500 130 1 365
## 2: 150 400 125 3 120
## 3: 150 400 NA 3 10
## 4: 159 200 140 2 730
## 5: 99 185 NA 30 200
## 6: 99 250 20 4 14
## availability_365 number_of_reviews review_scores_rating
## 1: 134 76 94
## 2: 315 17 94
## 3: 164 237 97
## 4: 0 18 97
## 5: 0 143 98
## 6: 0 702 95
## cancellation_policy Area neighbourhood
## 1: strict_14_with_grace_period Seattle Downtown
## 2: strict_14_with_grace_period Seattle Other neighborhoods
## 3: strict_14_with_grace_period Seattle Other neighborhoods
## 4: moderate Seattle Downtown
## 5: moderate Seattle Other neighborhoods
## 6: strict_14_with_grace_period Seattle Downtown
Other Features
There are many features that are relevant to the Airbnb rental price such as neighbourhood, number of bedrooms and number of accommodates.
Neighbourhood
Speaking of housing, most of the rental prices depend on the geographic feature. Houses in downtown are more expensive than those in suburb area. Further, the distance to shopping center or traffic station is also inneggligible if we try to list a fair rental price.
Leaflet mapping below shows the prices and names of different rental rooms in different neighbourhoods.
To give a better understanding of the price in different neighbourhoods, I plotted a heatmap (1) to show the average room prices in different neighbourhoods with different room types.
Next, from the heatmap(2), with the increase in the number of bedrooms, the average price of Airbnb listings in Seattle increase. Although it depends upon the neighbourhoods as well.
Number of Bedrooms
Number of bedrooms will always be a major factor to the rental price of Airbnb. I made a barplot to show the average prices over different number of bedroom. In this case, we can see from Figure 2 that there is a certain relationship between the average price of Airbnb listings and number of bedrooms.
Number of Accommodats
We can see thatnumber of accommodates have a certain effect on the rental price of Airbnb listings.
Room Type
In Airbnb listings, there are three types of room: Entire home/apt, Shared room and Private room. Room type is also a major factor of the price. Figure 4 shows the proportion of each of these three room type and we can see that there are nearly 74% of rooms are ‘Entire Room/Apt’. Further, Figure 5 below shows that ‘Entire room/apt’ have a higher average price than ‘Shared room’ and ‘Private room’.
